Step by step, explain the extended metaphor comparing the life span of the
nautilus and the progress of the human soul.
Explain the "stately mansions” (line 29), the
"low-vaulted past" (line 31), "each new
temple” (line 32), the "outgrown shell” (line
35), and the “unresting sea" (line 35).

This question seems to be incomplete. However, there is enough information to find the right answer.

The chambered nautilus is a cephalopod that has an external shell and, upon outgrowing it, will find another one that fits better. ]Once it leaves the smaller shell, it cannot return to it. This creature serves as a metaphor for the progress of the human soul, which grows through one´s lifespan until it also outgrows its shell, meaning the human body, and must change to a bigger shell, that of the spiritual level.

The author commands his soul to "Build thee more stately mansions," which symbolizes the creation of a better way of living. When he calls to "Leave thy low-vaulted past," we can infer that it´s a calling to leave behind a less spiritual life. In this context, the "outgrown shell" signifies the old ideas that are not suitable to the author anymore, due to "life’s unresting sea," which signifies the human lifetime.

Explanation:

The question refers to "The Chambered Nautilus” by Oliver Wendall Holmes.

An extended metaphor is a kind of metaphor that extends throughout multiple lines, or even throughout the entire poem, like in this example.